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An approximate martingale estimating function based on eigenfunctions is proposed for an estimation problem about an unknown drift parameter for a one-dimensional diffusion process with small perturbe...d parameter $ \varepsilon $ from discrete time observations at $ n $ regularly spaced time points $ k/n, k = 0, 1, cdots, n $. We study asymptotic properties of an M-estimator derived from the approximate martingale estimating function as $ \varepsilon \rightarrow 0 $ and $ n \rightarrow infty $ simultaneously.続きを見る
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